Abstract

This paper deals with the likelihood ratio test (LRT) for testing hypotheses on the mixing
measure in mixture models with
possibly unknown structural parameter. The main result gives the asymptotic distribution of the LRT statistics
under some conditions that are proved to be almost necessary.
A detailed solution is given for two testing problems: the
test of a single distribution against any mixture, with application to Gaussian, Poisson and
binomial distributions; the test of the number of populations in a
finite mixture with possibly unknown structural parameter.